1. Field of the Invention
This invention relates generally to the field of x-ray diffraction and, more specifically, to in-plane grazing incidence diffraction (IPGID).
2. Description of the Related Art
In the field of x-ray diffraction, radiation with a wavelength, λ, in the sub-nanometer range is directed to a crystalline material with a given interatomic spacing, d. When the angle of incidence, θ, relative to the crystalline structure satisfies the Bragg equation, λ=2d sin θ, an interferometrically reinforced signal (the diffracted signal), may be observed leaving the material, with an angle of emission being equal to an angle of incidence, both angles being measured with respect to a direction normal to the interatomic spacing of interest. The plane which is defined by the incident radiation and the diffracted signal is commonly referred to as the scattering plane.
If a material consists of a single crystal, all interatomic spacings of a specific length share the same orientation, meaning that the material must be precisely positioned such that the angle of incidence relative to the interatomic spacing of interest satisfies the Bragg equation. If a material is polycrystalline, that is, if it consists of multiple crystallites, the interatomic spacings will generally have random orientations and, thus, the material does not have to be precisely positioned for a diffraction analysis.
To enhance the diffraction signal emitted from the surface of a material, a geometry called in-plane grazing incidence diffraction (IPGID) may be used. In IPGID, the scattering plane is brought nearly coincident with the surface plane of the material. The deviation of the scattering plane from the material surface plane is called the “alpha angle.” For the incident beam, this angle is referred to as the “alpha incidence” (αI), while for the diffracted signal this angle is called the “alpha final” (αF). For an IPGID analysis, αI is set equal to or very near the angle of total external reflection of the material, giving the technique a significant increase of intensity. As this angle is typically very low, it also results in the beam being spread over the material surface, and a parallel plate collimator with a point detector is used to decouple low angle incident radiation spread from diffracted signal angle. This technique can be used to measure single crystal or polycrystalline regions of a material, as the in-plane incident radiation direction, θI, is decoupled from the scattering plane elevation angle, αI.